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Overshooting of Hypoplastic Models With Intergranular Strain: Manifestation, Implications and Remedy
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DOI：10.1002/nag.70375.png)
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Abstract
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Intergranular strain extensions of hypoplasticity (IGS, ISA, GIS) are widely used to model small-strain and cyclic soil behaviour. However, recent studies and our own simulations reveal that these models can exhibit stress overshooting not only under repeated small loading cycles but also during monotonic loading. This manifests as an unphysical accumulation of deviatoric stress and mobilised friction angles exceeding 60 ∘ $60^\circ$ , leading to overpredicted shear strength and stiffness. Of the three inspected extensions, IGS and ISA are the most susceptible to overshooting. While GIS mitigates overshooting under deviatoric loading, it persists during oedometric unloading-reloading. The cause lies in the constitutive structure of intergranular strain frameworks: when the mobilisation variable satisfies ρ < 1 $\rho <1$ , the effective elastic strain range becomes too large relative to the prevailing stress state, allowing stress accumulation with insufficient plastic dissipation. To regularise this behaviour while retaining the hypoplastic backbone, a two-step projection approach is proposed that activates only upon violation: (i) a deviatoric projection onto an auxiliary Matsuoka-Nakai surface with a state-dependent cut-off angle; and (ii) an isotropic projection that limits the mean effective stress to a state-dependent bounding pressure consistent with hypoplastic barotropy. Validation across four benchmark problems, including triaxial compression tests with monotonic loading and cyclic reloading, oedometric compression with unloading/reloading cycles and a laterally loaded pile, demonstrates that the projection is non-intrusive when the stress state remains admissible, and effectively regularises overshooting when it does not. The approach improves model robustness and physical consistency in simulations involving small-strain cycling or expanding plastic zones.
Keywords:
cyclic loading
hypoplasticity
intergranular strain
overshooting
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